Cocyclic designs give rise to relative
difference sets, and
vice versa [1]}.
Let \(E\)  be a group with normal
subgroup \(N\) , where \(|N|=n\)  and
\(|E:N|=v\) .
A \((v,n,k,\lambda )\) -relative
difference set in \(E\)  relative to \(N\)
(the forbidden subgroup)
is a \(k\) -subset \(R\)  of
a transversal for \(N\)  in \(E\)  such that
\(|R\cap xR|=\lambda \) 
for all \(x\in E\setminus N\) .
We call \(R\)  abelian if \(E\)  is
abelian, and splitting
if \(N\)  is a direct factor of \(E\) .
